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Mirrors > Home > ILE Home > Th. List > seqeq1 | Unicode version |
Description: Equality theorem for the sequence builder operation. (Contributed by Mario Carneiro, 4-Sep-2013.) |
Ref | Expression |
---|---|
seqeq1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iseqeq1 9919 |
. 2
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2 | df-seq3 9915 |
. 2
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3 | df-seq3 9915 |
. 2
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4 | 1, 2, 3 | 3eqtr4g 2146 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-sn 3456 df-pr 3457 df-op 3459 df-uni 3660 df-br 3852 df-opab 3906 df-mpt 3907 df-cnv 4460 df-dm 4462 df-rn 4463 df-res 4464 df-iota 4993 df-fv 5036 df-oprab 5670 df-mpt2 5671 df-recs 6084 df-frec 6170 df-iseq 9914 df-seq3 9915 |
This theorem is referenced by: seqeq1d 9925 seq3f1olemqsum 9990 iserex 10788 isumsplit 10946 ege2le3 11022 |
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